# Full Characterization of a Molecular Cooper Minimum Using High-Harmonic Spectroscopy

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{3}Cl), revealing a Cooper minimum (CM) analogous to the 3p CM previously reported in argon. The CM structure altered the spectral response and group delay (GD) of the emitted harmonics, and was revealed only through careful removal of all additional contributors to the GD. In characterizing the GD dispersion, also known as the “attochirp”, we additionally present the most complete validation to date of the commonly used strong-field approximation for calculating the GD, demonstrating the correct intensity scaling and extending its usefulness to simple molecules.

## 1. Introduction

_{3}Cl), which is analogous to the 3p orbital of argon. As we show, the CH

_{3}Cl CM was only clearly revealed through the combined analysis of XUV spectral intensity and phase.

_{4}), which is also structureless, and which has an ionization potential (IP) very similar to that of methyl chloride ($I{P}_{Xe}=12.13\mathrm{eV},I{P}_{C{H}_{4}}=12.61\text{}\mathrm{eV},\text{}I{P}_{C{H}_{3}Cl}=11.26\text{}\mathrm{eV}$ [21]). Finally, by comparing the HHG GD in methane and methyl chloride, we could isolate the contribution of the chlorine substitution to the RDME. This provides a robust method for isolating and diagnosing the signature of a CM without the need for complicated species-dependent calculations.

## 2. Materials and Methods

#### 2.1. Experimental Details

^{18}cm

^{−3}. In all cases, the molecules were probed in unaligned conditions, so any effects due to the permanent dipole [24] of methyl chloride were neglected due to angle averaging. The XUV light was propagated through a 200-nm aluminum filter to remove the remaining MIR, before being refocused into a home-built magnetic-bottle electron spectrometer (MBES). The MIR arm was recombined and focused, along with the XUV, in a gas jet in the MBES with variable delay, and the RABBITT interaction retrieved information about the XUV spectral phase from oscillations in the population of photoelectron sidebands at the energies of even harmonics. Neon was chosen as the detection gas due to its relatively uniform photoionization cross-section, and its GD contribution across the energetic range of interest (~30–70 eV) [25].

#### 2.2. High-Harmonic Spectral Analysis

## 3. Results and Discussion

#### 3.1. Intensity Scaling and Calibration

^{13}to 10.50 × 10

^{13}W/cm

^{2}, and the fitted recombination times (of which the derivative is the attochirp [20]) plotted as solid lines. For all scans, the GD from the aluminum filter and atomic detection gas were removed before fitting for the attochirp, such that only the laser intensity and an arbitrary offset were involved in the fitting. Because the focal geometry was unchanged when using different input powers, the laser intensity was expected to scale linearly with the measured power. This was tested by fitting the SFA intensity to the curve with the lowest energy, and, for the remainder of the datasets, by scaling using the measured input power, such that their ratios were fixed by the experiment. Details of the quality of the fit can be found in Appendix A, where it is shown that all datasets were, within experimental error, of zero deviation from the calculated SFA.

#### 3.2. Identifying the Cooper Minimum in Methyl Chloride

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

^{13}W/cm

^{2}to 10.50 × 10

^{13}W/cm

^{2}, the experimental result matched the calculation within experimental error, validating the calculation for its intended case of the atomic phase.

**Figure A1.**Mean error from the SFA fit in xenon. By applying the SFA fit to the lowest-intensity RABBITT data, and by scaling further calculations relative to the known input power, we found that the SFA calculations in xenon were, within error bars, of zero deviation from the experimental results.

^{13}W/cm

^{2}at 1.25 standard deviations from zero. Thus, we determined that the applicability to small molecules in the presented experiment was validated.

**Figure A2.**Mean error from the SFA fit in methane (CH

_{4}). By applying the SFA fit to the lowest-intensity RABBITT data, and by scaling further calculations relative to the known input power, we found that six of the seven SFA calculations in methane were, within error bars, of zero deviation from the experimental results, in spite of the calculation being designed to treat the atomic potential. The only outlier at 8.51×10

^{13}W/cm

^{2}sits 1.25 standard deviations from zero.

## References

- Krausz, F.; Ivanov, M. Attosecond physics. Rev. Mod. Phys.
**2009**, 81, 163–234. [Google Scholar] [CrossRef] - Marangos, J.P. Development of high harmonic generation spectroscopy of organic molecules and biomolecules. J. Phys. B At. Mol. Opt. Phys.
**2016**, 49, 132001. [Google Scholar] [CrossRef] - Haessler, S.; Fabre, B.; Higuet, J.; Caillat, J.; Ruchon, T.; Breger, P.; Carré, B.; Constant, E.; Maquet, A.; Mével, E.; et al. Phase-resolved attosecond near-threshold photoionization of molecular nitrogen. Phys. Rev. A
**2009**, 80, 011404(R). [Google Scholar] [CrossRef] - Huppert, M.; Jordan, I.; Baykusheva, D.; von Conta, A.; Wörner, H.J. Attosecond Delays in Molecular Photoionization. Phys. Rev. Lett.
**2016**, 117, 093001. [Google Scholar] [CrossRef] [PubMed] - Wörner, H.J.; Arrell, C.A.; Banerji, N.; Cannizzo, A.; Chergui, M.; Das, A.K.; Hamm, P.; Keller, U.; Kraus, P.M.; Liberatore, E.; et al. Charge migration and charge transfer in molecular systems. Struct. Dyn.
**2017**, 4, 061508. [Google Scholar] [CrossRef] [PubMed] - Kraus, P.M.; Mignolet, B.; Baykusheva, D.; Rupenyan, A.; Horný, L.; Penka, E.F.; Grassi, G.; Tolstikhin, O.I.; Schneider, J.; Jensen, F.; et al. Measurement and laser control of attosecond charge migration in ionized iodoacetylene. Science
**2015**, 350, 790–795. [Google Scholar] [CrossRef] [PubMed] - Cooper, J.W. Photoionization from Outer Atomic Subshells. A Model Study. Phys. Rev.
**1962**, 128, 681. [Google Scholar] [CrossRef] - Higuet, J.; Ruf, H.; Thiré, N.; Cireasa, R.; Constant, E.; Cormier, E.; Descamps, D.; Mével, E.; Petit, S.; Pons, B.; et al. High-order harmonic spectroscopy of the Cooper minimum in argon: Experimental and theoretical study. Phys. Rev. A
**2011**, 83, 053401. [Google Scholar] [CrossRef] - Carlson, T.A.; Krause, M.O.; Svensson, W.A.; Gerard, P.; Grimm, F.A.; Whitley, T.A.; Pullen, B.P. Photoelectron Dynamics of the Cooper Minimum in Free Molecules. Z. Phys. D At. Mol. Clust.
**1986**, 2, 309–318. [Google Scholar] [CrossRef] - Novak, I.; Benson, J.M.; Potts, A.W. UV Angle Resolved Photoelectron-Spectra of Fluoro and Chloromethane using Synchrotron Radiation. J. Electron. Spectrosc. Relat. Phenom.
**1986**, 41, 225–233. [Google Scholar] [CrossRef] - Holland, D.M.P.; Powis, I.; Ohrwall, G.; Karlsson, L.; von Niessen, W. A study of the photoionisation dynamics of chloromethane and iodomethane. Chem. Phys.
**2006**, 326, 535–550. [Google Scholar] [CrossRef] - Schoun, S.B.; Chirla, R.; Wheeler, J.; Roedig, C.; Agostini, P.; DiMauro, L.F.; Schafer, K.J.; Gaarde, M.B. Attosecond Pulse Shaping around a Cooper Minimum. Phys. Rev. Lett.
**2014**, 112, 153001. [Google Scholar] [CrossRef] [PubMed] - Wörner, H.J.; Niikura, H.; Bertrand, J.B.; Corkum, P.B.; Villeneuve, D.M. Observation of Electronic Structure Minima in High-Harmonic Generation. Phys. Rev. Lett.
**2009**, 102, 103901. [Google Scholar] [CrossRef] [PubMed] - Wong, M.C.H.; Le, A.T.; Alharbi, A.F.; Boguslavskiy, A.E.; Lucchese, R.R.; Brichta, J.P.; Lin, C.D.; Bhardwaj, V.R. High Harmonic Spectroscopy of the Cooper Minimum in Molecules. Phys. Rev. Lett.
**2013**, 110, 033006. [Google Scholar] [CrossRef] [PubMed] - Lewenstein, M.; Balcou, P.; Ivanov, M.Y.; L’Huillier, A.; Corkum, P.B. Theory of High-Harmonic Generation by Low-Frequency Laser Fields. Phys. Rev. A
**1994**, 49, 2117–2132. [Google Scholar] [CrossRef] [PubMed] - Mairesse, Y.; De Bohan, A.; Frasinski, L.J.; Merdji, H.; Dinu, L.C.; Monchicourt, P.; Breger, P.; Kovačev, M.; Taïeb, R.; Carré, B.; et al. Attosecond synchronization of high-harmonic soft x-rays. Science
**2003**, 302, 1540–1543. [Google Scholar] [CrossRef] [PubMed] - Kazamias, S.; Balcou, P. Intrinsic chirp of attosecond pulses: Single-atom model versus experiment. Phys. Rev. A
**2004**, 69, 063416. [Google Scholar] [CrossRef] - Mairesse, Y.; De Bohan, A.; Frasinski, L.J.; Merdji, H.; Dinu, L.C.; Monchicourt, P.; Breger, P.; Kovačev, M.; Auguste, T.; Carré, B.; et al. Optimization of attosecond pulse generation. Phys. Rev. Lett.
**2004**, 93, 163901. [Google Scholar] [CrossRef] [PubMed] - Varjú, K.; Mairesse, Y.; Carré, B.; Gaarde, M.B.; Johnsson, P.; Kazamias, S.; López-Martens, R.; Mauritsson, J.; Schafer, K.J.; Balcou, P.H.; et al. Frequency chirp of harmonic and attosecond pulses. J. Mod. Opt.
**2005**, 52, 379–394. [Google Scholar] [CrossRef] - Doumy, G.; Wheeler, J.; Roedig, C.; Chirla, R.; Agostini, P.; DiMauro, L.F. Attosecond Synchronization of High-Order Harmonics from Midinfrared Drivers. Phys. Rev. Lett.
**2009**, 102, 093002. [Google Scholar] [CrossRef] [PubMed] - Lias, S.G. Ionization Energy Evaluation. In NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Linstrom, P.J., Mallard, W.G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, USA, 2005. Available online: https://webbook.nist.gov/cgi/cbook.cgi?Contrib=L (accessed on 10 June 2018).
- Paul, P.M.; Toma, E.S.; Breger, P.; Mullot, G.; Augé, F.; Balcou, P.; Muller, H.G.; Agostini, P. Observation of a train of attosecond pulses from high harmonic generation. Science
**2001**, 292, 1689–1692. [Google Scholar] [CrossRef] [PubMed] - Muller, H.G. Reconstruction of attosecond harmonic beating by interference of two-photon transitions. Appl. Phys. B
**2002**, 74, S17–S21. [Google Scholar] [CrossRef] - Etches, A.; Madsen, L.B. Extending the strong-field approximation of high-order harmonic generation to polar molecules: Gating mechanisms and extension of the harmonic cutoff. J. Phys. B At. Mol. Opt. Phys.
**2010**, 43, 155602. [Google Scholar] [CrossRef] - Mauritsson, J.; Gaarde, M.B.; Schafer, K.J. Accessing properties of electron wave packets generated by attosecond pulse trains through time-dependent calculations. Phys. Rev. A
**2005**, 72, 013401. [Google Scholar] [CrossRef] - Rakić, A.D. Algorithm for the determination of intrinsic optical constants of metal films: Application to aluminum. Appl. Opt.
**1995**, 34, 4755–4767. [Google Scholar] [CrossRef] [PubMed] - Dahlström, J.M.; Guénot, D.; Klünder, K.; Gisselbrecht, M.; Mauritsson, J.; L’Huillier, A.; Maquet, A.; Taïeb, R. Theory of attosecond delays in laser-assisted photoionization. Chem. Phys.
**2013**, 414, 53–64. [Google Scholar] [CrossRef] - Lin, C.D.; Le, A.-T.; Chen, Z.; Morishita, T.; Lucchese, R. Strong-field rescattering physics-self-imaging of a molecule by its own electrons. J. Phys. B At. Mol. Opt. Phys.
**2010**, 43, 122001. [Google Scholar] [CrossRef] - Frolov, M.V.; Manakov, N.L.; Sarantseva, T.S.; Starace, A.F. Analytic formulae for high harmonic generation. J. Phys. B At. Mol. Opt. Phys.
**2009**, 42, 035601. [Google Scholar] [CrossRef] - Boutu, W.; Haessler, S.; Merdji, H.; Breger, P.; Waters, G.; Stankiewicz, M.; Frasinski, L.J.; Taieb, R.; Caillat, J.; Maquet, A.; et al. Coherent control of attosecond emission from aligned molecules. Nat. Phys.
**2008**, 4, 545–549. [Google Scholar] [CrossRef] - Diveki, Z.; Camper, A.; Haessler, S.; Auguste, T.; Ruchon, T.; Carré, B.; Salières, P.; Guichard, R.; Caillat, J.; Maquet, A. Spectrally resolved multi-channel contributions to the harmonic emission in N
_{2}. New J. Phys.**2012**, 14, 023062. [Google Scholar] [CrossRef] - McFarland, B.K.; Farrell, J.P.; Bucksbaum, P.H.; Gühr, M. High Harmonic Generation from Multiple Orbitals in N
_{2}. Science**2008**, 322, 1232–1235. [Google Scholar] [CrossRef] [PubMed] - Le, A.-T.; Morishita, T.; Lin, C.D. Extraction of the species-dependent dipole amplitude and phase from high-order harmonic spectra in rare-gas atoms. Phys. Rev. A
**2008**, 78, 023814. [Google Scholar] [CrossRef] - Jin, C.; Le, A.-T.; Lin, C.D. Medium propagation effects in high-order harmonic generation of Ar and N
_{2}. Phys. Rev. A**2011**, 83, 023411. [Google Scholar] [CrossRef] - Farrell, J.P.; Spector, L.S.; McFarland, B.K.; Bucksbaum, P.H.; Gühr, M.; Gaarde, M.B.; Schafer, K.J. Influence of phase matching on the Cooper minimum in Ar high-order harmonic spectra. Phys. Rev. A
**2011**, 83, 023420. [Google Scholar] [CrossRef] - Gaarde, M.B.; Buth, C.; Tate, J.L.; Schafer, K.J. Transient absorption and reshaping of ultrafast XUV light by laser-dressed helium. Phys. Rev. A
**2011**, 83, 013419. [Google Scholar] [CrossRef]

**Figure 1.**Laser intensity scaling in xenon. Measured extreme ultraviolet (XUV) group delays (circles) are shown from harmonic generation in xenon gas, fitted with intensities as shown in the legend. The lowest-intensity curve was fitted for intensity using Equation (9), and this fitted intensity was scaled according to the measured input power ratio for each additional scan (curves). Each intensity was separated by 0.2 fs for visual clarity.

**Figure 2.**Laser intensity scaling in methane. Measured XUV group delays (circles) are shown from harmonic generation in methane, fitted with intensities as shown in the legend. As with the xenon scan of Figure 1, the lowest-intensity curve was fitted according to Equation (9), and scaled by the measured input power ratio for each additional scan (curves). Each intensity was separated by 0.2 fs for visual clarity.

**Figure 3.**Influence of the methyl chloride Cooper minimum (CM) on the spectral intensity relative to methane. (

**a**) Normalized spectra were taken in sequence with identical harmonic generation conditions for the intensity comparison of methane (blue) and methyl chloride (green); (

**b**) The ratio of normalized spectra from (

**a**) shows the relative minimum in amplitude. Because the laser field was held constant and the spectra were normalized, the difference was attributable exclusively to the chlorine substitution.

**Figure 4.**Methane and methyl chloride comparison. Methane (blue) and methyl chloride (green) group delays are shown with the filter and atomic delays removed. (

**a**) The strong-field approximation (SFA) group delay (red) is shown along with the high-harmonic contribution (${\mathsf{\tau}}_{HHG}$) from the experiment. The SFA intensity was fit using methane, resulting in an intensity of 5.56 × 10

^{13}W/cm

^{2}, and then, this same intensity was applied to the methyl chloride data. The methyl chloride data are shown with a −0.2-fs shift for visual clarity. (

**b**) After removal of the SFA curve, ${\mathsf{\tau}}_{target}$ was isolated. By doing so, the CM in methyl chloride was revealed as a ~120-as structure in group delay. (

**c**) Group delays were then integrated to show the phase shift of approximately 2.6 radians across the CM.

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**MDPI and ACS Style**

Scarborough, T.D.; Gorman, T.T.; Mauger, F.; Sándor, P.; Khatri, S.; Gaarde, M.B.; Schafer, K.J.; Agostini, P.; DiMauro, L.F.
Full Characterization of a Molecular Cooper Minimum Using High-Harmonic Spectroscopy. *Appl. Sci.* **2018**, *8*, 1129.
https://doi.org/10.3390/app8071129

**AMA Style**

Scarborough TD, Gorman TT, Mauger F, Sándor P, Khatri S, Gaarde MB, Schafer KJ, Agostini P, DiMauro LF.
Full Characterization of a Molecular Cooper Minimum Using High-Harmonic Spectroscopy. *Applied Sciences*. 2018; 8(7):1129.
https://doi.org/10.3390/app8071129

**Chicago/Turabian Style**

Scarborough, Timothy D., Timothy T. Gorman, François Mauger, Péter Sándor, Sanjay Khatri, Mette B. Gaarde, Kenneth J. Schafer, Pierre Agostini, and Louis F. DiMauro.
2018. "Full Characterization of a Molecular Cooper Minimum Using High-Harmonic Spectroscopy" *Applied Sciences* 8, no. 7: 1129.
https://doi.org/10.3390/app8071129